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AP Calculus Notebook Daniel and Cory
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1.
Limits of Functions (including one-sided limits)
Calculating limits using algebra
Estimating limits from graphs or tables using data
Asymptotic and unbounded behavior (vertical and horizontal asymptotes)
Describing asymptotic behavior in terms of limits involving infinity
2.
Continuity
When is a function continuous at a point x = a?
Understanding continuity in terms of limits
Intermediate Value Theorem
3.
Differential Calculus
What is a derivative?
Definition of the derivative of a function
Definition of the derivative at a point x = a
Relationship between differentiability and continuity
Tangent lines vs. Normal lines
Theorems on Differentiation (power, chain, etc.)
First Derivative Test
Second Derivative Test
Mean Value Theorem
Rolle’s Theorem
Absolute vs. Relative Extrema
Rectilinear Motion Problems
Implicit Differentiation
Related Rates
Optimization
Given the graph of f ′(x), sketch a possible graph of f(x)
Use of the calculator
4.
Integral Calculus
Antiderivatives
Indefinite Integrals: Polynomial, Trig, Logs/Exp
Definite Integrals: Fundamental Theorem of Calculus Parts I and II
Integration Techniques: Power, Chain, Log/Exp, u-substitution
Properties of Definite Integrals
Riemann Sum Definition
Estimating Area using Rectangles (left, right, midpoint) and Trapezoids
Area
Volumes of solids of revolution
Volume with known cross sections
Average Value/Mean Value Theorem for Integrals
Differential Equations (Separation of Variables)
Slope Fields
Use of the calculator
What is a derivative?
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A derivative is the slope of a function at a given point x=a.
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